On the existence and uniqueness of JML estimates for the partial credit model

A necessary and sufficient condition is given in this paper for the existence and uniqueness of the maximum likelihood (the so-called joint maximum likelihood) estimate of the parameters of the Partial Credit Model. This condition is stated in terms of a structural property of the pattern of the data matrix that can be easily verified on the basis of a simple iterative procedure. The result is proved by using an argument of Haberman (1977). The author wishes to thank the Editor and the anonymous reviewers for their comments that helped to substantially improve the final version of this paper. This research was supported in part by a MURST grant (ex 60%).     

The profession of ferryman: Considerations on the analyst's internal attitude in consultation and in referral1

Psychoanalytic consultation is an interview with a patient who will not be taken in treatment by the consultant analyst, but who will be sent to another, perhaps specifi cally chosen, colleague after one or more assessment sessions. This practice is becoming increasingly important since, besides traditional private relationships between consultant and patient, it is now common in many specialized centres affi liated to offi cial psychoanalytical institutions. The author explores some fundamental aspects of the analyst's internal attitude in consultation: motivation to know; a ‘concave’ attitude to listening; responsibility in proposing suitable technical choices and referral to a further specialist; empathy and partial identifi cation; the balance between authentic experience in the consultation and risks of seduction; internal links within the community of colleagues; the technique for sending patients on. He presents a clinical example, specifi cally aimed at reproducing the internal attitude of the analyst, together with the necessary work that allows a diffi cult patient to initiate psychoanalytic treatment.     

Knowledge on Treelike Spaces

This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability for this system.     

A Note on Prototypes,Convexity and Fuzzy Sets

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy.     

Detecting local convexity on the pareto surface

Recent regain in interest in multi‐criteria optimization approaches to provide a designer with multiple solutions to select from and support decisions has led to various methodologies to generate such solutions and possibly approximate the Pareto set. This paper introduces the notions of H‐ and w‐convexities, and develops a simple method to identify local convexity of Pareto hyper‐surfaces since their shape can dictate the choice of the method to use to obtain Pareto solutions and possibly to build an approximation of that set. The method is based on comparing the results from the weighting method to those of the Tchebycheff method at any point on the Pareto hyper‐surface. If, under some conditions, the points obtained from the two methods are identical or not, a local convexity or its lack can be assumed at that location and in its immediate neighbourhood. A numerical example is included. Copyright © 2002 John Wiley & Sons, Ltd.     

Equidiscrimination Contours around an Achromatic Colour Are Convex but Not Balanced

A model based on the postreceptor channels followed by a Minkowski norm (Minkowski model) is widely used to fit experimental data on colour discrimination. This model predicts that contours of equal discrimination in colour space are convex and balanced (symmetrical). We have tested these predictions in an experiment. Two new statistical tests have been developed to analyse convexity and balancedness of experimental curves. Using these tests we have found that while they are in line with the convexity prediction, our experimental contours strongly testify against balancedness. It follows that the Minkowski model is, generally, inappropriate to model colour discrimination data.